In message <7c73d2b3-584d-4481-a690-ff26bfa7673d@googlegroups.com>, Paul <pepstein5@gmail.com> writes>I think I can offer a tiny further improvement in your simplification >as follows. In contrast to Rado, the set on which we show canonicity >is B(4) rather than B(2). Your lemma 1 can then be used unchanged >because B(4) is a subset of B(2). This approach lets us omit the step: >[Replace X and X' by X_0 and X_1 from [B(4)]^r such that (X,X') = >(X_0,X_1)]>>Does this work as a further simplification or does it simplify too >much, and thereby introduce an error?

I think that would work. Rado's "PQ lemma" needs to proved for all B', my lemma for B = B(2) and then the final result in B(4).-- David Hartley